# What is Young's modulus: Definition and 189 Discussions

Young's modulus

E

{\displaystyle E}
, the Young modulus, or the modulus of elasticity in tension, is a mechanical property that measures the tensile stiffness of a solid material. It quantifies the relationship between tensile stress

σ

{\displaystyle \sigma }
(force per unit area) and axial strain

ε

{\displaystyle \varepsilon }
(proportional deformation) in the linear elastic region of a material and is determined using the formula:

E
=

σ
ε

{\displaystyle E={\frac {\sigma }{\varepsilon }}}
Young's moduli are typically so large that they are expressed not in pascals but in gigapascals (GPa).
Although Young's modulus is named after the 19th-century British scientist Thomas Young, the concept was developed in 1727 by Leonhard Euler. The first experiments that used the concept of Young's modulus in its current form were performed by the Italian scientist Giordano Riccati in 1782, pre-dating Young's work by 25 years. The term modulus is derived from the Latin root term modus which means measure.

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1. ### Determine equivalent Young's Modulus

We need to find a single wire supporting the load. But, when I think about it there can so many different types of materials we could use for the single wire and each of these single wires would have a different Young's Modulus. So, I don't get what equivalent means here? Anyways, I get the...
2. ### Relationship between diameter and elastic potential energy of a wire

I think the answer is that the elastic potential energy will be a 1/16th of the original value. This is my reasoning: 1) If the diameter doubles, the cross sectional area is 4 times the original value. (from A= πr2). 2) F= stress/area. Force (load is the same). If cross sectional area...
3. ### B Suggestions for Internal Assessment Project on Young's Modulus

Hi. I am in the IB and am looking at doing a physics IA (internal assessment) on Young's modulus on an elastic material. I was thinking of doing it on the the stretchy snakes like the candy. What would I need to cover in this?
4. ### Young's Modulus of a Banana leaf

Summary:: What is Young's modulus of banana leaf in MPa? What is Young's modulus of banana leaf in MPa? [Thread moved from the technical forums, so no Schoolwork Template is shown]
5. ### B Why is Young's modulus constant below the limit of proportionality?

Hi all, I'm a little confused about something. Force-extension graphs and stress-strain graphs are always both straight lines up until the limit of proportionality, implying both the spring constant and the Young modulus are constant up until then. For a force-extension graph, Hooke's Law...
6. ### What Chemical Properties Affect Young's Modulus?

I can't seem to figure out which chemical properties govern the physical property that is young's modulus. For example, any linear (or with a low degree of branching) polyethylene with no crosslinking is still a somewhat rigid and solid substance (higher ym), whereas the most linear possible...
7. ### Biophysics Q: Impact of stiffness (Young's modulus) on stress failure

Hi. I'm a physician trying to understand the micromechanics of lung injury due to overdistension. The basic idea is that overstretching of the plasma membrane of the lung epithelial cell causes "stress failure" --> i.e. plasma membrane rupture --> cell death. The concepts of stress, strain, and...
8. ### Young's Modulus and the Poisson Ratio of Aluminium

Hi. I've been given these sets of value. How do I calculate Young's modulus and Poisson Ratio from these set of value. I tried to create a stress vs strain graph but the graph does not look like a common stress vs strain graph but instead more of a y=x graph. The diameter of the rod is 10mm and...
9. ### Question involving Young's modulus (mass hanging from a wire)

so what I did wrong?
10. ### Definition of Young's modulus

I just found a definition to the Young modulus as: Is this a plausible representation of Y? That is, i know the definition , i don't think we can say this definition and the first definition is equal.
11. ### Young's modulus and compression

See this figure: The rod is put at first between A and B shims without comprehension, suddenly a force is applied at R from an axis as the figure points. Find Fa and Fb. (the figure is a look from above) This can be solved by consider the "constant elastic" of the shims equal, but my...
12. ### Calculating Young's Modulus from this Stress/Strain Graph

I am trying to calculate Young's Modulus on the graph below. I have run the test through some software, now want to calculate Young's Modulus to ensure my analysis can be relied upon to be scientifically sound. This is what i have calculated from learning online. Is this correct? I have 2 more...
13. ### Young's modulus: Stress, Strain and Force for a Steel Bar

As all attempts to get it right but without success this is one of the problems with my workout . Where i did wrong calculations ? The questions got the answers in brackets.
14. ### Calculating Force Using Young's Modulus

How can you Calculate Force ?
15. ### Young's modulus question with answer notation issue

Summary:: why this answer ? I have the result of a young s modulus that is 358280256.25 and the answer the teacher gave us is 3.58 x 10 to the power of 8 . why not 358.3 x 10 to the power of 6 ? how she s deciding how many steps goes back with the point , the answer of a sum before this...
16. ### Maths for Sound passing through different mediums

What is the mathematics involved with calculating the energy lost from sound as it passes through different mediums? If I started off with a 70dB(A) sound wave, and after 0.5m it passed through 10mm of mild steel - what would be the sound level (in dB) 1m away from the steel plate? To clarify...
17. ### Young's modulus — Finding the change in the length of a metal bar under stress

A steel bar 6.00 m long and with rectangular cross section of 5.00 cm x 2.50 cm supports a mass of 2000 kg. How much is the bar stretched ? (the young s modulus of steel is 20 x 10 n\m squared)
18. ### Measuring Tensile Strength in an alternative way

So I've been looking at a few material tests and they all start with a rectangular sample of the material, loaded into a machine which extends them by increasing load at a constant rate and measures the strain/stress till the point of material fracture. The yield stress is measured in usually...
19. ### Manipulating equation for Young's Modulus and Hooke's Law

Equating the two equations gives me ##k = -\frac {YA}{L}## but the correct answer of the same magnitude but opposite sign. I think the nub of my misunderstanding is quite elementary (who would have guessed!) : When is it ##F=kx## and when is it ##F=-kx##? If I understand correctly, F is the...
20. ### Mechanics of Solids - weight problem

Summary: How much weight can the bars support? Three one-meter-long bars with cross-section area A = 1 square centimeter support a rigid plate of weight W. For steel, E = 200 GPa and S = 400 MPa. Determine the maximum weight W the bars can support for three cases: (i) all three bars are...
21. ### Young's Modulus, Stress/Strain graph and Calculating Energy

For part (b), I counted the number of squares underneath the 2 day sample to be roughly 33 'whole' squares (the 5by5 tiny squares is 1 whole sqaure). I then equated 33 whole square = 0.35 MJ to calculate 1 whole square to be 0.0106 MJ. I then counted the number of whole squares underneath the...
22. ### I Resonant frequencies of a membrane, dependance on Young's modulus?

Hello, natural frequencies of (circular) membrane are expressed in every textbook as: where is the m-th positive root of the Bessel Function of the first kind of order n. For m=1, n=0: ξmn = 2,405. represents the radius of membrane, and is the velocity of wave propagation...
23. ### Thermal Expansion of a Wire Connected To a Rod

Homework Statement Homework Equations ΔL=LαΔT σ=EΔL/L The Attempt at a Solution For part a, I used the coefficient of linear expansion for copper and the change in temperature to find the change in length (0.068%). I thought part b had the same answer. The two are attached, and I would...
24. ### Calculating Dimensions of Titanium Disk Under Load

Homework Statement A titanium disk (with ##E=107 ~GPa##, Poisson's ratio, ##v=0.34##) precisely ##l_0=8~mm## thick by ##d_0=30~mm## diameter is used as a cover plate in a mechanical loading device. If a ##P=20~kN## load is applied to the disk, calculate the resulting dimensions, ##l_{01}## and...
25. ### Difference Between Young's Modulus & Second Moment of Area

Hi all I was hoping someone could help explain the difference between Young's Modulus and Second Moment of Area. I know that Young's modulus is a measure of how elastic a material is and is calculated by Stress/Strain. I know that the Second Moment of Area can be defined as a objects...
26. ### Young's modulus of a steel post, finding change in length

Homework Statement Superman pulls on a steel post to trap a supervillian. The post has a cross-sectional area of 30cm^2 and a length of 2m. If Superman applies a force of 6X10^6N by how much is the length of the post increased? A) 2mm B) 7mm C) 1.2cm D) 1.7cm E) 2cm Homework Equations...
27. ### Young's Modulus Experiment With a Glass Screen

Homework Statement Homework Equations Path difference is nλ at maxima, (n+0.5)λ at minima The Attempt at a Solution I think the phase difference between S1 and S2 is not 0 anymore, because the wave effectively takes a longer distance by going through S2. Thus, there is no longer a central...
28. ### Relationship of Young's modulus and impulse force

Homework Statement Is that possible to obtain the a relationship between Young's modulus of a spring and impulse force with below information ? I personally think that we cannot if without the given cross-sectional area A and the given spring constant k. The particle is connect to a elastic...
29. ### A Calculating Young's modulus

I need to calculate Young's modulus based on deformation of sphere into ellipsoid. I assume the deforming force acting along one axes. Initial dimensions of the object before (sphere) and after (ellipsoid) deformation are known.Does anyone know or familiar with good reference?
30. ### Find out the Young's modulus of a carbon fiber lamina composite

Hello everyone, nice to be here. I am going to calculate the young modulus of 3 layers of carbon fiber laminar composite For example: 1st: 12K plain wave carbon fiber in 0 degree 2nd:3K till wave carbon fiber in 45deg 3rd:12K plain wave carbon fiber in 0 degree How can I approach to calculate...
31. ### Relationship between thickness, width and length

1.A rectangular steelbar of length subjected to tensile force of 80kN. Calculate the change in length if the width and thickness are (40 & 25)mm respectively. (E = 207 GN/m2). Homework Equations E= stress/strain stress = F/A; F =80kN strain = dL/L 3. I just want to know what to use for the...
32. ### Young's modulus and uncertainty

Homework Statement Homework EquationsThe Attempt at a Solution Y = (F/A)/(∆L/L) = FL/A∆L Putting values of F , L , A and simplifying Y = 2×109/∆L I don't know how to proceed . I also don't understand what is uncertainty in length and uncertainty in strain . Is uncertainty the same thing...
33. ### B Young's Modulus and Stiffness

Just want clarification on two equations. So basically, I want to calculate the time period T of the complete oscillation of a cantilever. I use this equation. Is E equal to young's modulus or is it equal to stiffness? If it is equal to stiffness, can I use this equation to calculate the...
34. ### Determining Young's Modulus of Aluminium from Tensile Test

My Aim is to determine the youngs modulus of aluminium from the data we get from tensile strength test. The attached excel sheet contains all the data i am using such as elongation,load value(which is in kN i have converted to N for calculating Stress) For stress, I am using the formula...
35. ### Finding the elastic modulus of a metal in a mixed phase

Homework Statement If a metal is adhered to a surface of another metal, let's say copper is plated onto aluminum, how can the elastic modulus of copper can be extracted given only the data of the thickness of the copper and aluminum, the young's modulus of the combined metal and the modulus of...
36. ### Relation between Young's modulus and the coefficient of thermal expansion

Is it true for all material that if young's modulus is high then melting point will be high and coeff of thermal expansion will be lower? Any example that doesn't follow the above statement. Many Thanks
37. ### Young's Modulus of 3 Metals

Homework Statement hi guys I am conducting an experiment for my coursework in physics and i have come across a bit of a problem. i am trying to calculate the youngs modulus of 3 different metals Aluminium steel and brass. To calculate the modulus of the material i am using a chart of Mass k/g...
38. ### Young's modulus equation

Homework Statement I'm doing an experiment to determine the young's modulus involving the following equation: Homework Equations The Attempt at a Solution Finding the base units of the young's modulus with the equation resulted in the young's modulus being dimensionless, which of course is...
39. ### Experimentally Determined Young's Modulus

Homework Statement [/B] So in my mechanics of materials lab, we calculated Young's modulus after measuring the strain and applying force to a beam. What I'm trying to figure out is, why are you able to use both a bending force and an axial force when calculating Young's modulus? Homework...
40. ### Young's Modulus Brass Wire Question

Homework Statement A 10 kg load suspended by a brass wire 10 m long is observed to vibrate vertically in SHM at a frequency of 10 vib/s. Given that the Young's modulus for brass is , what is the cross-sectional area of the wire? So we know: m = 10kg l = 10m f = 10Hz Y = 9x10^10 Homework...
41. ### Young's Modulus problem

Homework Statement A particle mass m moves in a straight line on a smooth horizontal table, and is connected to two points A and B by light elastic springs of natural lengths 2l_{o} and 3l_{o} , respectively, and modulus of elasticity λ . The points A and B are a distance 6l_{o}...
42. ### B A statistical definition of Young's Modulus?

Young's Modulus is usually defined as the intrinsic property of a material indicating it's stiffness, or it's ability to resist deformation. Though, it is measured in Pa, meaning it should have some statistical description. Spring constant, for example, can be define as the stiffness of an item...
43. ### Difference between Young's Modulus and spring constant?

I have read that Young's Modulus, like spring constant, is a measure of stiffness (how hard it is to deform a material). Though apparently, Young's Modulus is a way of doing so that applies only to the material and not its shape, where a spring constant value depends on the dimensions of the...
44. ### Traction/ Compression stress and strain exercise

Hello everyone, could you help me with this exercise? I am stuck, and I can't find anything on the internet that solves this. Your help is very much appreciated :) 1. Homework Statement Circular steel bar, clamped at extremities. Two parts: A(ab)=800mm² A(bc)=400mm² L(ab)=...
45. ### Measuring young's modulus from simple harmonic motion

Homework Statement I was doing this experiment: http://practicalphysics.org/shm-cantilever.html I'm interested in the derivation of the result ω^2 = Exy^3 / 4*M*L^3. I tried to think where it comes from. How do we even start to derive k from the equation mg = KS where S is the delta in the...
46. ### A Find Young's modulus of quantum well semiconductor

Hi How to find young's modulus of quantum well semiconductor? For GaAs- young's modulus E=85 GPa and For Al0.3Ga0.7As- young's modulus E=84 GPa. For quantum well Al0.3Ga0.7As/GaAs/Al0.3Ga0.7As Value of young's modulus is?
47. ### Young's Modulus Formula / Steel Cable

A steel cable 3.00 cm 2 in cross-sectional area has a mass of 2.40 kg per meter of length. If 500 m of the cable is hung over a vertical cliff, how much does the cable stretch under its own weight? Take Y steel ϭ 2.00 ϫ 10 11 N/m 2 .Y=([L][/o]F)/(A*delta_L) My attempt of solution...
48. ### Calculate Stress & Strain from Length, Diameter & Load

Unsure how to calculate in order to get the stress (N/mm2) and strain (%) if: a material has a length of 50mm diameter of 12mm Load: 11.5 kN Extension 0.025 mm Help on how to work this out would be very appreciated :)
49. ### A Young's modulus graphene nanoribbons

Young’s modulus is given as the second derivative of the total energy with respect to the strain divided by the equilibrium volume. Can help me for the calculate equilibrium volume and young's modulus?
50. ### Femur Compression/Young's Modulus

Homework Statement By what amount does the 52-cm-long femur of an 73 kg runner compress at this moment? The cross-section area of the bone of the femur can be taken as 5.2×10-4 m2 and its Young's modulus is 1.6×1010 N/m2. Express your answer to two significant figures and include the...